Exceptional figure of merit achieved in boron-dispersed GeTe-based thermoelectric composites

GeTe is a promising p-type material with increasingly enhanced thermoelectric properties reported in recent years, demonstrating its superiority for mid-temperature applications. In this work, the thermoelectric performance of GeTe is improved by a facile composite approach. We find that incorporating a small amount of boron particles into the Bi-doped GeTe leads to significant enhancement in power factor and simultaneous reduction in thermal conductivity, through which the synergistic modulation of electrical and thermal transport properties is realized. The thermal mismatch between the boron particles and the matrix induces high-density dislocations that effectively scatter the mid-frequency phonons, accounting for a minimum lattice thermal conductivity of 0.43 Wm−1K−1 at 613 K. Furthermore, the presence of boron/GeTe interfaces modifies the interfacial potential barriers, resulting in increased Seebeck coefficient and hence enhanced power factor (25.4 μWcm−1K−2 at 300 K). Consequently, we obtain a maximum figure of merit Zmax of 4.0 × 10−3 K−1 at 613 K in the GeTe-based composites, which is the record-high value in GeTe-based thermoelectric materials and also superior to most of thermoelectric systems for mid-temperature applications. This work provides an effective way to further enhance the performance of GeTe-based thermoelectrics.


Part I. Single Parabolic Band (SPB) modeling
According to the single parabolic band model 1,2 , thermoelectric properties are given by Seebeck coefficient Hall carrier concentration Electrical thermal conductivity is calculated according to the Wiedemann-Franz law 3 , where L represents the Lorentz number.L is given by where kB is the Boltzmann constant, e is the electron charge, S is the Seebeck coefficient, nH is the carrier concentration, and λ is the constant, respectively.λ is dependent on scattering factor r, which is equal to r+1/2.Assuming acoustic phonon scattering dominating the carrier scattering, r = -1/2.
when the scattering factor taken into account, Part II.Debye-Callaway's model Umklapp scattering process: Normal process: Grain boundaries scattering: Point defects scattering: Dislocation scattering 4,5 : Nano precipitates phonon scattering 5,6 : τtot is the total relaxation time, namely: In the above equations, γ is the Grüneisen parameter, β is the ratio between normal process and Umklapp phonon scattering, υ is the Poison ratio, V is the average atomic volume, M is the average atomic mass, Γ is the point defect scattering parameter, d is the grain size, a is the lattice parameter, and Ns is the number of stacking faults crossing a line of unit length, BD is Burgers' vector, ND is the density of dislocations, R is the average radius for the precipitates D is the matrix density, ΔD is density difference between the precipitate and matrix, Np is the number density of precipitates, A is the domain fitting parameter, dDB is the average domain width respectively.
V and M referred to literatures 7 , and γ and υ have been calculated by sound velocity v. Np, Ns, ND and d were measured via TEM characterization.D and ΔD were calculated according to the theorical crystal structure.

Part III. Density functional theory (DFT) calculations
Density functional theory (DFT) calculations are performed using the plane-wave pseudopotential method in the Vienna Ab initio Simulation Package (VASP) [8][9][10][11] .The projector augmented wave (PAW) potentials are used to describe the interaction between electrons and ions.Generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) is employed to describe the exchange and correlation functions 12 .A 3×3×2 supercell based on the primitive cell of rhombohedral GeTe (Ge18Te18) and a supercell with one Ge atom replaced by Bi (Ge17BiTe18) are created to calculate band structure.A Monkhorst-Pack with 3×3×5 k-grid and cutoff energy of 450 eV are applied to represent the integration in the Brillouin zone of the electronic structure.Band-unfolding technique is utilized to unfold high-symmetry points to first Brillouin zone with PyVaspwfc tool 13 , and the spin-orbit coupling (SOC) effect is considered throughout the band calculation with 0 magnetic moment of all atoms.

Table 2 .
Rietveld refinement parameters, doping dependent lattice parameters, unit cell volume, and the refinement agreement factors for BixGe0.99-xTe-By wt.% samples at 300 K.

Table 4 .
Parameters for phonon modeling studies